Large Language Models (LLMs) have demonstrated strong reasoning ability in open-domain question answering, yet their reasoning is typically expressed through linear textual traces, such as Chain-of-Thought (CoT). While these traces are readable, their sequential form can obscure logical dependencies, making inconsistencies difficult to inspect. Existing graph-based methods introduce structured representations, but they often rely on externally provided graphs, leaving it unclear whether LLMs can autonomously perform graph-structured reasoning. To fill this gap, we explore graph-structured reasoning of LLMs in general-domain question answering. We propose Self-Graph Reasoning (SGR), a framework that enables LLMs to explicitly represent their reasoning process as a structured graph before producing the final answer, improving both consistency and interpretability. We further construct a graph-structured reasoning dataset that merges multiple candidate reasoning graphs into refined graph structures for model training. Experiments on five QA benchmarks across both general and specialized domains show that SGR consistently improves reasoning consistency and provides clearer, more interpretable graph-structured reasoning processes, achieving a 17.74% gain over the base model.